Dr. Deepak Gumber
Associate Professor

Designation:

Associate Professor

Specialization:

Algebra

Email:

dkgumber@thapar.edu

Research Interests

Finite Groups, Automorphisms of Finite Groups

Sponsored Research Projects

Sr.No. Sponsor Title of Project Duration Grant Amount
1. UGC Automorphisms of Finite p-Groups 2014-17 60 Lakhs
2. NBHM Non-Inner and Class-Preserving Automorphisms of Finite p-Groups 2014-17 10.11 Lakhs
3. SERB, DST Divisibility Conjecture and Existence of Non-Inner Automorphisms of Order p for Non-Abelian Finite p-Groups 2016-19 20.56 Lakhs

PhD Students

Sr.No. Name of Student Title of Thesis Year
1. Hemant Kalra Automorphisms of Finite p-Groups 2013
2. Mahak Sharma Central and Class-Preserving Automorphisms of Finite p-Groups 2015
3. Sandeep Singh Automorphisms of Finitely Generated Groups 2016

Research Publications

  • Sandeep Singh and Deepak Gumber, Automorphism groups of finitely generated groups that are isomorphic to the group of inner automorphisms, Quaestiones Mathematicae (to appear).
  • Mahak Sharma, Hemant Kalra and Deepak Gumber, Some finite p-groups with central automorphism group of non-minimal order, J. Algebra Appl. 17(2) (2018) 1850026 (5 pages).
  • Sandeep Singh and Deepak Gumber, A note on commuting automorphisms of finite p-groups, Math. Notes 100(5) (2016), 755- 757.
  • Sandeep Singh, Deepak Gumber and Hemant Kalra, Erratum: IA-automorphisms of finitely generated nilpotent groups, J. Algebra Appl. 15(7) (2016), 1692002 (2 pages).
  • Deepak Gumber and Hemant Kalra, Equality of certain automorphism groups of finite p-groups, J. Algebra Appl. 15(3) (2016), 1650056 (7 pages).
  • Sandeep Singh and Deepak Gumber, Finite p-groups whose absolute central automorphisms are inner, Math. Commun. 15 (2015), 1-6.
  • Deepak Gumber and Hemant Kalra, The conjugacy class number k(G): a different perspective, Comm. Algebra, 43(11) (2015), 4836-4838.
  • Mahak Sharma and Deepak Gumber, Class-preserving automorphisms of some finite p-groups, Proc. Indian Acad. Sci. (Math. Sci.), 125(2) (2015), 181-186.
  • Deepak Gumber and Hemant Kalra, Finite p-groups with central automorphism group of minimal order, Comm. Algebra, 43(5) (2015), 1802-1806.
  • Sandeep Singh, Deepak Gumber and Hemant Kalra, IA-automorphisms of finitely generated nilpotent groups, to appear in J. Algebra Appl.
  • Hemant Kalra and Deepak Gumber, A note on conjugacy classes of finite groups, to appear in Proc. Indian Acad. Sci. (Math. Sci.).
  • Deepak Gumber and Hemant Kalra, On the converse of a theorem of Schur, Arch. Math., 101 (2013) 17-20.
  • Mahak Sharma and Deepak Gumber, On central automorphisms of finite p-groups, Comm. Algebra, 41 (2013) 1117-1122.
  • Hemant Kalra and Deepak Gumber, On equality of central and class preserving automorphisms of finite p-groups, Indian J. Pure Appl. Math., 44(5) (2013) 711-725.
  • Deepak Gumber, Some applications of augmentation quotients, Hacet. J. Math. Stat., 42 (6) (2013) 627-631.
  • Deepak Gumber, An intersection theorem in free group rings, Int. J. Algebra, 4 (2010) 769-775.
  • Deepak Gumber, Ram Karan and Indu Pal, Some augmentation quotients of integral group rings, Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008) 537-546.
  • Ram Karan and Deepak Kumar, Augmentation quotients of free group rings, Algebra Colloq., 12 (2005) 597-606.
  • Ram Karan, Deepak Kumar and L. R. Vermani, Some intersection theorems and subgroups determined by certain ideals in integral group rings, II, Algebra Colloq., 9 (2002) 135-142.
  • Ram Karan and Deepak Kumar, Some intersections and identifications in integral group rings, Proc. Indian Acad. Sci. (Math. Sci.), 112 (2002) 289-297.

Honours/Awards/Fellowships

  1. UGC Research Award in 2013
  2. CSIR Junior and Senior Research Fellowship during PhD
  3. University Research Fellowship during PhD
  4. Haryana State Merit Scholarship during MA

Invited Talks

  1. Finite p-groups with central automorphism group of minimal order, Discussion Meeting on Group Theory, May 8-11, 2014, IISER, Mohali.
  2. A Note on Conjugacy Classes of Finite Groups, International Conference on Group Theory and Lie Theory (GT & LT-2012), March 19-21, 2012, Harish-Chandra Research Institute, Jhunsi, Allahabad.
  3. Augmentation Quotients of Integral Group Rings, Colloquium on Recent Trends in Algebra and Algebraic Number Theory, November 25-27, 2009, Center for Advanced Studies in Mathematics, Panjab University, Chandigarh.

Conferences/Workshops Attended

  1. Attended and presented a paper entitled “On Class Preserving Automorphisms of Groups of Order 32” in “International Workshop cum Conference on Groups, Actions, Computations-2010” held from Sep. 10-12, 2010 in Harish Chandra Research Institute, Allahabad.
  2. Presented a paper entitled “An Intersection Theorem in Free Group Rings” in “International Conference on Algebra and its Applications” held from Nov. 13-16, 1997 in Dept. of Mathematics, Aligarh Muslim University, Aligarh.
  3. Presented a paper entitled “Some Intersection Theorems and Subgroups Determined by Certain Ideals in Integral Group Rings” in “Sixth Ramanujan Symposium on Algebra and its Applications” held from Feb. 24-26, 1999 in Ramanujan Institute for Advanced Study in Mathematics, University of Madras.
  4. Attended “International Conference on Algebra and its Applications” held from Nov. 13-16, 1997 in Dept. of Mathematics, Aligarh Muslim University, Aligarh.